PLACE VALUE AND WHOLE NUMBERS

Every Number in its Place

Our math text books tell us that the number system we use when we do mathematics is a place value number system. What does that mean? Let's study the first 2 words in the phrase to find out. Place Value -- tells us that the value of a number depends on where it is placed.

5 (five) means 5 × 1 because the 5 is in the one's place
500 (five hundred) means 5 × 100 because the 5 is in the hundred's place
and 5 000 000 (5 million) means 5 × 1 000 000 because the 5 is in the million's place

The value of each place or column is 10 times the value of the place or column next to it on the right. Let's look at a place value chart to discover how this works.

Reading and Writing Numbers Correctly

1) reading numbers the right way:

We notice when we first learn to say numbers that there are special names for the decades -- the numbers in the 10's column (1-digit multiples of 10). We say two hundred when we see 200, but we don't say 2 ten when we see 20 -- we say twenty. The number 3 536 is said three thousand, five hundred, thirty-six. Notice how we say thirty and not 3 ten. The same is true once we pass the 1000's column. When we see 26 000, we say twenty-six thousand not 2 ten thousands, 6 thousand. This number 159 000 is read one hundred fify-nine thousand.

A common mistake when saying numbers is to use "and" where we shouldn't. Most people will say one hundred AND fify-nine thousand for 159 000 -- but it is not correct since we use the word "and" to indicate the decimal point. $6.73 should be read six dollars AND seventy-three cents but 6030 is not read or said six thousand AND thirty. We say six thousand thirty unless we mean 6 000.30 -- then we say AND. This number 504 is read five hundred, four -- not five hundred AND four.

2) writing numbers the right way:

Before the days of large-scale international trade, different countries used different ways of writing numbers. A common practice in English speaking countries was to use the British approach to large numbers. To make big numbers easier to read, we used commas (,) to separate groups of 3 digits, counting from the right end (decimal point) like this: 132, 576, 964. However, now that the countries of the world are standardizing how numbers are written (displayed), and many European countries (especially France and Belgium) use the comma ( , ) rather than the point ( . ) to indicate the decimal, we can no longer use it to separate triples of numbers.
If we write 3, 507 to mean three thousand five hundred seven, someone from France might think it means 3.507. To avoid confusion, those of us who use the decimal point no longer use the comma to mark off groups of 3 digits. We now use a space where the comma would be like this: 19 201.3 instead of 19, 201.3. In Canada, this poses a special problem because Quebec uses the French approach and the rest of the country uses the British method. In Quebec, if our phone bill was $21.50 we'd see 21, 50$ on the "amount owing" line in the bill.

Note: your text and work books might still use the comma notation, but it is going out of use. In the USA today, both systems are accepted, however, we should try to adopt world standards when we can. If your teacher expects to see commas in large numbers, put them in.

Comparing and Ordering Whole Numbers

When we need to know the largest or smallest in a group of numbers, it's very easy to decide. We look at them from left to right since the biggest place values -- the 10-thousands, thousands, and hundreds -- are at the left end of our place value chart. The number with the largest digit in the column farthest left is the biggest, and the number with the smallest digit in the column farthest left is the smallest.

The symbols we use to compare numbers are less than ( < ), greater than ( > ) or equal to ( = ). A good way to remember which one means bigger than and which means smaller than is to look at the symbol. We see a small side (the point or vertex) and a big side (the "mouth"). The less than symbol < starts small at a point and ends big or wide -- so it means smaller than -- because it starts out small. The greater than symbol > starts big and becomes small, so it means bigger than. Actually, we can read these symbols correctly from either direction.

If we read 5 > 3 from left to right it says 5 is bigger than 3
and if we read it from right to left, it says 3 is smaller than 5.
The statement is true if we read it in either direction.

So we see that when we meet the pointy end first, it means smaller than, and when we meet the wide or big mouth first, it means bigger than.

Examples

1) Write these numbers with digits:
a) four thousand fifty-five = 4 055 b) thirty-seven thousand six = 37 006

c) nine hundred sixty-three = 963 d) two hundred thirteen thousand = 213 000

2) Write these numbers in words:
a) 6 017 = six thousand seventeen b) 27 109 = twenty-seven thousand, one hundred nine

c) 506 = five hundred, six d) 401 000 = four hundred one thousands

3) Write the value of each underlined digit as a number and a word:
a) 12 895
value is 2 000
two-thousand
b) 64 927
value is 60 000
sixty-thousand
c) 5 813
value is 800
eight hundred
d) 122 371 995
value is 20 000 000
twenty-million

4) Write the place name of each underlined digit:
a) 12 895
thousands place
b) 64 927
ten-thousands place
c) 5 813
ones place
d) 122 371 995
hundred-millions place

5) Write < , > , or = , between the numbers:
a) 004 __ 4

ones: 4 equals 4 so,

004 = 4

b) 101 __ 109

hundreds: 1 = 1
tens: 0 = 0
ones: 1 less than 9, so

101 < 109

c) 72 __ 58

tens: 7 more than 5, so

72 > 58

d) 128 __ 170

hundreds: 1 = 1,
tens: 2 less than 7, so

128 < 170

Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.

Practice

1) Write each of these numbers in a place value chart:
a) 40 thousand, sixteen b) 9 million, 7 hundred, six c) 4 hundred, 8 thousand, sixty-four

2) Write these numbers in words:
a) 90 022 b) 215

c) 105 006 d) $40.20

3) Write the value of each underlined digit as a number and a word:
a) 121 895
b) 64 927
c) 2 567 813
d) 1220

4) Write < , > , or = , between the numbers:
a) 1 128 __ 1 170 b) 101 ___ 99 c) 72 ___ 0072 d) 5 125 ___ 5 120 e) 34 ___ 43

Solutions

1) write these numbers in a place value chart:

a) 40 thousand, sixteen

b) 9 million, 7 hundred, six

c) 4 hundred, 8 thousand, sixty-four

2) Write these numbers in words:

a) 90 022 = ninety thousand, twenty-two b) 215 = two hundred, fifteen

c) 105 006 = one hundred five thousand, six d) $40.20 = forty dollars AND twenty cents

3) Write the value of each underlined digit as a number and a word:

a) 121 895
value is 90
ninety
b) 64 927
value is 4 000
four thousand
c) 2 567 813
value is 500 000
five hundred thousand
d) 1220
value is 200
two hundred

4) Write < , > , or = , between the numbers:

a) 1 128 < 1 170 b) 101 > 99 c) 72 = 0072 d) 5 125 > 5 120 e) 34 < 43

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